{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,18]],"date-time":"2026-09-18T08:08:48Z","timestamp":1789718928390,"version":"4.0.1"},"reference-count":17,"publisher":"Society for Industrial & Applied Mathematics (SIAM)","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["SIAM J. Numer. Anal."],"published-print":{"date-parts":[[2008,1]]},"abstract":"<jats:p>We consider the incompressible Navier\u2013Stokes equations where on a part of the boundary flow rate and mean pressure boundary conditions are prescribed. There are basically two strategies for solving these defective boundary problems: the variational approach (see J. Heywood, R. Rannacher, and S. Turek, Internat. J. Numer. Methods Fluids, 22 (1996), pp. 325\u2013352) and the augmented formulation (see L. Formaggia, J. F. Gerbeau, F. Nobile, and A. Quarteroni, SIAM J. Numer. Anal., 40 (2002), pp. 376\u2013401, and A. Veneziani and C. Vergara, Internat. J. Numer. Methods Fluids, 47 (2005), pp. 803\u2013816). However, both of these approaches present some drawbacks. For the flow rate problem, the former resorts to nonstandard functional spaces, which are quite difficult to discretize. On the other hand, for the mean pressure problem, it yields exact solutions only in very special cases. The latter is applicable only to the flow rate problem, since for the mean pressure problem it provides unfeasible boundary conditions. In this paper, we propose a new strategy based on a reformulation of the problems at hand in terms of the minimization of an appropriate functional. This approach allows us to treat the two kinds of problems (flow rate and mean pressure) successfully within the same framework, which can be useful in view of a mixed problem where the two conditions are simultaneously prescribed on different artificial boundaries. Moreover, it is more versatile, being prone to be extended to other kinds of defective conditions. We analyze the problems obtained with this approach and propose some algorithms for their numerical solution. Several numerical results are presented supporting the effectiveness of our approach.<\/jats:p>","DOI":"10.1137\/060672005","type":"journal-article","created":{"date-parts":[[2008,7,23]],"date-time":"2008-07-23T14:45:10Z","timestamp":1216824310000},"page":"2769-2794","source":"Crossref","is-referenced-by-count":39,"title":["A New Approach to Numerical Solution of Defective Boundary Value Problems in Incompressible Fluid Dynamics"],"prefix":"10.1137","volume":"46","author":[{"given":"Luca","family":"Formaggia","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Alessandro","family":"Veneziani","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Christian","family":"Vergara","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"351","published-online":{"date-parts":[[2008,7,3]]},"reference":[{"key":"R1","doi-asserted-by":"publisher","DOI":"10.1137\/S0363012999351097"},{"key":"R2","doi-asserted-by":"publisher","DOI":"10.3934\/dcdsb.2006.6.1077"},{"key":"R3","doi-asserted-by":"publisher","DOI":"10.1051\/m2an:2005044"},{"key":"R4","doi-asserted-by":"publisher","DOI":"10.1137\/S003614290038296X"},{"key":"R5","doi-asserted-by":"publisher","DOI":"10.1007\/s007910050030"},{"key":"R6","doi-asserted-by":"publisher","DOI":"10.1007\/BF01399323"},{"key":"R7","doi-asserted-by":"crossref","unstructured":"M. Gunzburger,\n                      Perspectives in Flow Control and Optimizations\n                      , SIAM, Philadelphia, 2003.","DOI":"10.1137\/1.9780898718720"},{"key":"R8","unstructured":"F. Hecht, O. Pironneau, F. Le Hyaric, and K. Ohtsuka,\n                      Freefem++\n                      , www.freefem.org."},{"key":"R9","doi-asserted-by":"publisher","DOI":"10.1002\/(SICI)1097-0363(19960315)22:5<325::AID-FLD307>3.0.CO;2-Y"},{"key":"R10","doi-asserted-by":"publisher","DOI":"10.1137\/S0036142901384009"},{"key":"R11","doi-asserted-by":"crossref","unstructured":"V. Martin, F. Cl\u00e9ment, A. Decoene, and J. F. Gerbeau,\n                      Parameter identification for a one-dimensional blood flow model\n                      , in Proceedings of Cemracs 2004, ESAIM, Les Ulis, Vol. 14, 2005, pp. 174\u2013200.","DOI":"10.1051\/proc:2005014"},{"key":"R12","unstructured":"S. A. Nazarov and K. Pileckas,\n                      Asymptotic conditions at infinity for the Stokes and Navier-Stokes problems in domains with cylindrical outlets to inifnity\n                      , in Advances in Fluid Dynamics, P. Maremonti, ed., Quaderni di Matematica Seconda Universit\u00e0 di Napoli, Aracne ed. Caserta, 1999."},{"key":"R13","doi-asserted-by":"publisher","DOI":"10.1137\/S1540345902408482"},{"key":"R14","unstructured":"A. Veneziani,\n                      Boundary conditions for blood flow problems\n                      , in Proceedings of ENUMATH, Rannacher et al.  eds., World Scientific Publishing, River Edge, NJ, 1998."},{"key":"R15","doi-asserted-by":"publisher","DOI":"10.1002\/fld.843"},{"key":"R16","doi-asserted-by":"publisher","DOI":"10.1016\/j.cma.2006.09.011"},{"key":"R17","unstructured":"C. Vergara,\n                      Numerical Modeling of Defective Boundary Problems in Incompressible Fluid-Dynamics\u2014Applications to Computational Haemodynamics\n                      , Ph.D. thesis, Politecnico di Milano, 2006; available online from http:\/\/mox.polimi.it."}],"container-title":["SIAM Journal on Numerical Analysis"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/epubs.siam.org\/doi\/pdf\/10.1137\/060672005","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,21]],"date-time":"2026-08-21T15:14:13Z","timestamp":1787325253000},"score":1,"resource":{"primary":{"URL":"https:\/\/epubs.siam.org\/doi\/10.1137\/060672005"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2008,1]]},"references-count":17,"journal-issue":{"issue":"6","published-print":{"date-parts":[[2008,1]]}},"alternative-id":["10.1137\/060672005"],"URL":"https:\/\/doi.org\/10.1137\/060672005","relation":{},"ISSN":["0036-1429","1095-7170"],"issn-type":[{"value":"0036-1429","type":"print"},{"value":"1095-7170","type":"electronic"}],"subject":[],"published":{"date-parts":[[2008,1]]}}}